1,376 research outputs found
Computational Aspects of the Hausdorff Distance in Unbounded Dimension
We study the computational complexity of determining the Hausdorff distance
of two polytopes given in halfspace- or vertex-presentation in arbitrary
dimension. Subsequently, a matching problem is investigated where a convex body
is allowed to be homothetically transformed in order to minimize its Hausdorff
distance to another one. For this problem, we characterize optimal solutions,
deduce a Helly-type theorem and give polynomial time (approximation) algorithms
for polytopes
Data-driven and Model-based Verification: a Bayesian Identification Approach
This work develops a measurement-driven and model-based formal verification
approach, applicable to systems with partly unknown dynamics. We provide a
principled method, grounded on reachability analysis and on Bayesian inference,
to compute the confidence that a physical system driven by external inputs and
accessed under noisy measurements, verifies a temporal logic property. A case
study is discussed, where we investigate the bounded- and unbounded-time safety
of a partly unknown linear time invariant system
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
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